Characters with powerful telekinesis are portrayed as being able to exert a superhuman force using only their minds. For example, they can throw a car.

Based on what I remember from high school physics, throwing a 2000 kg vehicle to 10 m/s requires an impulse of 20000 N⋅s. But Newton's 3rd Law states that momentum is always conserved and every action has an equal and opposite reaction. So exerting a 20000 N⋅s impulse—whether by gravitational, magnetic, or other means—would throw an 80 kg superhero backwards at 250 m/s. Even if they could survive that, it would be awfully inconvenient to walk back to the battlefield.

No violation of Newton's 3rd law has ever been observed by experiment, so even saying that our hero can draw on a vast energy source doesn't solve the problem.

So how could our hero throw a car without also throwing himself? Can the momentum be put somewhere else? Or is there a way for our hero to use his powers to protect himself from harm?

Note: I'm not looking for a scientific explanation for where the superpower itself comes from, just a little logical consistency. Truth be told, I mostly want a headcanon for when I watch X-Men films.

$\begingroup$Or just throw another car in the opposite direction :]$\endgroup$
– RudolfJelinJun 9 at 7:24

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$\begingroup$Not the first time I answer this, but I advise you to read "Mistborn" of Brandon Sanderson. The characters don't exactly have telekinesy but can push or pull on anything metallic with their minds and it follows the 3rd law the same way. It could give you inspiration for your work.$\endgroup$
– EchoxJun 9 at 10:10

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$\begingroup$All it reminds me of is Eddings' books. They DO generate energy from nowhere so they can counteract the third law, but the first time Belgarion tries to lift a rock, he ends up pushing himself into the ground in doing so. Over time, he learns to use part of his energy to also push himself up and counteract Newton's third law (they don't call it that.... but yeah)$\endgroup$
– PatriceJun 10 at 12:21

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$\begingroup$@Patrice I am recalling it a bit better. My reaction to that was in response to having recently done some yardwork. To sink as far into the ground as he did would have required more than just "soft" ground. It would have required ground so deeply muddy as to be approaching quicksand in consistancy.$\endgroup$
– Michael RichardsonJun 11 at 17:58

11 Answers
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Basically, they would subconsciously learn to simultaneously exert an equal and opposite force spread out over a much larger area behind them or anywhere else that isn't the car they're throwing. A sign of an amateur telekinetic could be being thrown back by their 'throws' because they haven't learnt to do this yet. The area would be so large the force would be spread out such that that anyone in it couldn't tell someone was using telekinesis without precise scientific equipment.

A true master, optionally The One True Master, can focus that opposite force into a second useful target. Example use cases are smashing enemies into each other in combat, or, more grimly, tearing an enemy apart.

$\begingroup$Great answer. Perhaps surprisingly, this is all that's really called for. Also, on the flip side of the amateur telekenetic, you may have a fascinating school of thought dedicated to identifying the signature of this spread out force, identifying where the telekenetic is, what school they studied under, and how much force they were exerting.$\endgroup$
– Cort AmmonJun 8 at 21:23

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$\begingroup$@willk it can't. You can store energy in massive batteries, but youcan't store linear momentum except by actually moving. Although I do suppose you could have a really heavy rock orbiting Earth and use that as your momentum sink instead of using Earth itself. Warning: excessive use may cause Moon to crash into Earth or to escape into deep space, both of which have non-negligible chance of reducing human population by up to and including 100%.$\endgroup$
– John DvorakJun 9 at 11:47

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$\begingroup$@John - Elastic potential energy is not momentum. You can convert momentum to energy and store it as electricity in a battery just the same.$\endgroup$
– DavorJun 9 at 13:31

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$\begingroup$I’m very much reminded of the first Discworld books, where wizards had to be very careful to balance telekinetic spells lest they accidentally flick their own brain out of their ears.$\endgroup$
– Joe BloggsJun 9 at 17:15

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$\begingroup$This is exactly how the power is handled in the Mistborn trilogy by Brandon Sanderson. It works remarkably well and even introduces plot.$\endgroup$
– user400188Jun 10 at 1:57

Here's a rudimentary description of a Field Effect Transistor (FET): Imagine water moving through a pipe. When the gate value is all the way open, water flows through the pipe freely. As you close the gate valve, the water through the pipe is restricted until the valve is finally closed and no water can flow. The magic? It takes a lot less water energy to open and close the valve than is represented by the water flowing through the pipe.

Why is this important? Because that's the basic operation of an amplifier. A little effort is applied to open or close the valve, but it controls a lot of water. And if you track the opening and closing of the valve over time (say it looks like a Sine wave, smoothly opening and closing, back and forth...), and then track the water flow through the pipe — you'll find that it's the very same Sine wave but MUCH BIGGER! Woot!

Now, let's apply this to your telekinesis

What your superhero is actually doing is acting like the base or gate of a transistor. He/she is creating/managing a channel of force between, let's say, the rotational momentum of the Earth and the object (oh, let's say Hoover Dam) to be tossed about. But your superhero isn't channeling that force directly. He/she is simply setting up the channel, and then controlling it as the gating function.

A little effort in, the destruction of Laughlin, Nevada out. Maybe a minor stress headache as a result. You know, the mental equivalent of a tired wrist from turning a screwdriver too many times.

But my superhero can't be godlike!

Absolutely not! But even FETs have limits. They can't channel infinite amounts of electricity. Superheros with this ability come in many sizes! Some can gate/control enough of the Earth's rotational momentum to kick a poodle. Others have no trouble slinging cars around. There was that one dude, Whackismo! back in the 50s... he actually diverted an incoming meteor! Which was COOL! Right up until the governments of the world figured that not only could he easily rip the doors off of Fort Knox, but that his saving of the world actually made days measurably longer.... People figure the last time anybody heard from him was October 3, 1956.

It's probably best that we forget. We'd hate for Majestic 12 to think anybody was remembering him.

Wait... did you say the days got longer?

Oh, yeah. There's a consequence to drawing energy from the Earth's rotational momentum. If you draw enough of it, the rotation slows down and days get longer. You could draw it from Earth's orbital momentum, but then the years would get longer. Technically you could draw it from Earth's solar trajectory momentum, but that would probably cause the Earth to slowly change its orbital elliptic — you know, the angle of the orbit compared to the rest of the planets. That could be fun.

$\begingroup$sweet! Best telekinesis explanation I have read. I wonder if Whackismo could use the momentum of the car as relative to the sun, not the Earth. The car stops moving and the Earth continues along out from underneath it. I suppose it is all about frame of reference, like everything is.$\endgroup$
– WillkJun 9 at 1:09

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$\begingroup$@Willk, that's not a bad idea. Every time the telekinetic does something, the (theoretically minor) disturbance in the sun's momentum plays with it's big magnetic field and causes a solar flare. It would be a way of introducing the telekinetic to the government in the story. "Mr. President, have you ever noticed that the solar flares seem to coincide with your daughter's weird temper tantrums? You know, the ones you've said we're never supposed to talk about?"$\endgroup$
– JBHJun 9 at 18:29

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$\begingroup$Couldn't he simply use Earth's rotational momentum in either direction (deceleration/ accelerating), and over time even the influence out? [Not all cars need to be flung westwards?]$\endgroup$
– AganjuJun 9 at 18:50

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$\begingroup$@Aganju, You're thinking in terms of bracing against the physical Earth. But that's not what's being proposed. Using energy in the "slow the Earth down" direction draws energy out. To "spin the Earth faster" requires putting energy in. It's not an issue of direction so much an issue of the flow of energy - like a battery. You can't expend energy to throw a car and speed the world up at the same time without drawing energy from someplace else to do both.$\endgroup$
– JBHJun 10 at 0:39

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$\begingroup$When slinging a car, you slow the earth down. But unless you put the car on an escape trajectory, it will get slowed by air resistance/crash/whatever, putting that energy back into the planet. Only in the case of things escaping the influence of the earth there might be problems - such as in the case of diverting asteroids. You can still choose in what direction to affect it though.$\endgroup$
– Daniel VestølJun 10 at 12:00

Frame Challenge: My Invisible Friend Joe

You’re looking at this the wrong way. If I tell my friend Joe to go pick up a rock and throw it, and he does, I will never experience the associated ‘equal and opposite reaction’ because I’m not the one doing the throwing.

You’re imagining telekinesis as reaching out an invisible arm from yourself, and assuming that arm has to then also push you back when you use it, but there’s no reason telekinesis has to work that way. Detach the arm! Think of it like having an invisible friend named Joe who happens to really like doing stuff you tell him to do, and is more than happy to throw a few cars around if you ask nicely.

Joe follows the third law, of course, but Joe follows the third law the way that a tornado picking up a car does. It doesn’t get thrown back, it just loses a little of its existing momentum.

Fun twists

This also lets you experiment with fun story beats about Joe turning out to be less metaphorical than you initially thought. Nothing more distressing than discovering your telekinesis can be grumpy, or on vacation on another planet.

Or, even better, why have one Joe when it could be an army of invisible flying pixies?

Not entirely answering the question, but Newton's Third Law isn't the only problem here. A far greater problem is conservation of energy. Lifting a 1 tonne car against gravity by 1m needs 10kJ of potential energy. Accelerating that car to 10m/s needs 50kJ of potential energy.

Several other answers have actually covered where this energy might come from. Unfortunately they've confused momentum and energy. It's important to be clear which is which!

The character Molly in Runaways has another solution. Her telekinesis is powered by her body's stored energy reserves (if they'd wanted to get technical, they could have mentioned glycogen, but they didn't really need to). So after lifting something heavy, she's exhausted like she's just run a marathon, and she goes to sleep. It's one of the few instances I've seen where a superhero actually follows physical laws.

$\begingroup$You'd be surprised just how much energy humans can store in their chemistry. Your 10kJ energy expenditure example can only power a human for 1.3 days.$\endgroup$
– John DvorakJun 9 at 11:51

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$\begingroup$@JohnDvorak Oh, absolutely, and that's why I like the example of Molly. We have plenty of stored energy (some more than others round the waistline ;) but we can't get to all that energy very quickly. What we can get to, we get tired if we use it up. So the energy budget is actually reasonable for telekinesis to be run by the same body chemistry as muscles, but like muscles, when you work them hard then you need a rest after.$\endgroup$
– GrahamJun 9 at 22:37

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$\begingroup$Conservation rarely is a problem when talking about magic because unless the author specifically explains that magic uses the bodily reserves, there's often a secondary source that replenishes itself by magical means.$\endgroup$
– EchoxJun 10 at 14:25

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$\begingroup$Another Discworld example; in Wintersmith Tiffany uses the heat from a fire to melt snow. The magic isn't in generating the heat, its directing it at the particular bit of snow she wants to melt while standing 100 yards from the fire.$\endgroup$
– Paul JohnsonJun 11 at 13:56

$\begingroup$@PaulJohnson Yes, I like how Pterry handles that. You might be better to make that an answer in its own right. It's pretty similar to JBH's answer along the same kind of lines, but JBH focusses on momentum.$\endgroup$
– GrahamJun 11 at 14:36

You can store momentum kind of like the way a capacitor can store energy. The momentum density of the electric and magnetic field is
$$\frac1{c^2}\vec S=\epsilon_0\vec E\times\vec B$$
where $\vec E$ is the electric field, $\vec B$ is the magnetic field and $\epsilon_0=8.85\times10^{-12}\,F/m$ is the permittivitiy of free space. So if a being had an organ where they[?] could create and maintain sufficiently strong electric and magnetic fields, they could change their momentum without changing velocity.

The problem is that the dielectric strength of air is about $3\times10^6\,V/m$ and $1\,T$ is a pretty strong magnetic field, about the most you can get with a NdFeB magnet, and $1\,L=10^{-3}\,m^3$ is about as much volume as a human-sized being could reasonably invest in such an organ so this would work out to about $2.7\times10^{-8}\,kg\cdot m/s$ so it would only be a sufficient momentum reserve to perhaps win a few bets at a Belter bar before the other patrons got wise to you, but hardly in the ballpark of throwing cars around.

Not to mention that it may turn out that the sources of the electric and magnetic fields have to have equal and opposite momentum to that which was created in the internal organ...

$\begingroup$Not gonna lie, I do not really understand the physics here. But your the discussion of electromagnetic fields got me thinking—photons have momentum, right? So could our dilemma be solved, in theory, by firing a beam of light in the opposite direction?$\endgroup$
– CheezeyJun 10 at 3:30

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$\begingroup$They are trying to refute the comment of @JohnDvorak where he said you can't store momentum like a battery stores energy. You don't know by chance which Belter bar he frequents, do you? Thus a photon rocket wouldn't work for them because they would be spitting out momentum in an obvious detectable way. Now, you might propose a neutrino rocket but that's not really what they're trying to achieve in my post.$\endgroup$
– user5713492Jun 10 at 3:40

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$\begingroup$@Cheezey See this xkcd What If? article. You could do the photon thing, but the energy requirements would be absolutely astronomical.$\endgroup$
– SanchisesJun 11 at 9:55

$\begingroup$Also, while this answer may be correct, you now have a protagonist that is slowly moving backwards with huge momentum. You still have to transfer this momentum somehow to another object like the ground, so really, you only delay the problem rather than fixing it.$\endgroup$
– SanchisesJun 11 at 9:55

... magic had indeed once been wild and lawless, but had been tamed
back in the mists of time by the Olden Ones, who had bound it to obey
among other things the Law of Conservation of Reality; this demanded
that the effort needed to achieve a goal should be the same regardless
of the means used. In practical terms this meant that, say, creating
the illusion of a glass of wine was relatively easy, since it involved
merely the subtle shifting of light patterns. On the other hand,
lifting a genuine wineglass a few feet in the air by sheer mental
energy required several hours of systematic preparation if the wizard
wished to prevent the simple principle of leverage flicking his brain
out through his ears.

$\begingroup$Welcome to WorldBuilding.SE! While this perfectly illustrates the problem that OP is trying to solve, the only part that actually answers it is "several hours of systematic preparation", and that's not very specific at all. What would this "systematic preparation" entail?$\endgroup$
– F1KrazyJun 10 at 22:09

$\begingroup$Welcome to Worldbuilding.SE! We're glad you could join us! When you have a moment, please click here to learn more about our culture and take our tour. This is an excellent example of somebody else's rules of magic, but it doesn't actually answer the question.$\endgroup$
– JBHJun 11 at 3:48

1

$\begingroup$I'm sorry this doesnt comply to the worldbuilding.se guidelines, I just wanted to share this quote because it's about the same topic. Cheers.$\endgroup$
– GuestJun 11 at 19:15

If you pick up 100lbs in telekinesis then you would have to simultaneously redirect that 100lbs of force elsewhere or it will instead be exerted on the psychic. Effectively telekinesis would be an invisible arm connected to you and you have to use a second arm to distribute the weight elsewhere, unless you want to become beastly strong.

Or perhaps your telekinesis requires you to set 2 predetermined points for weight distribution. If you pick up a car all you are doing is making an expanding telekinetic pillar under the car which is distributing the weight downwards. If you want to throw it while its in the air then you have to connect the car to a nearby building and exert equal force on the car and the building. If the buildings walls are weak then you may just punch a hole in the building and not move the car much. That could get pretty complex when thinking about it but might actually make for interesting tactical fights.

A wormhole near the object, connects to a place with strong gravity (eg. Jupiter). The gravitational field pulls the object, and all you do is control the location (and existence) of the wormhole.

Caution: If the wormhole gets too big, material will pass through it. Put on end at the bottom of the Marianas Trench, and you get a high pressure stream that can probably cut through concrete. Best to keep "standard" wormhole size smaller than a water molecule.

Why does it have to avoid violating the Third Law at all? Newton's laws are not really laws, but simply an approximation and are known to be incomplete. There are a variety of situations where they don't apply.

Telekinesis is, by definition, "spooky action at a distance," so we're already throwing Newtonian physics out the window by invoking it and moving into more accurate descriptions of the world such as quantum mechanics and relativity.

The best way for your telekinetic heroes to avoid the 3rd law is to reframe telekinesis not as imparting a force, but as changing the reference frame definition of the action. Newtonian mechanics are only valid in inertial reference frames, so the easiest thing to do is to say telekinesis creates a non-inertial reference frame.

The most common example of this is gravity. An object in a gravitational field doesn't feel a force of gravity acting on it, it feels an acceleration. A force is defined as F=ma, meaning that the force an object "feels" is affected by the mass of another object pushing it. To figure out how an object moves in response to a force, you divide the force by its mass and get the acceleration: a = F/m.

But gravity works differently. Regardless of an object's mass, it always experiences the same acceleration; a feather and a hammer fall at the same speed and hit the ground at the same time when dropped from the same height in a vacuum. This fact is why scientists often call gravity a "fictitious force," in that it is indistinguishable from an acceleration caused by any other means (rocket, elevator, guy pushing you down the street, etc...). When you're in freefall towards the Earth, you're not pushing on the Earth, nor is it pushing on you, you're merely accelerating towards each other. Newton himself noticed this disturbing fact about gravity but said "leave it to someone else to figure out." Eventually, Einstein did, and he found that objects always want to move in "a straight line" between two points, or more accurately, "the shortest-time path." This is called a brachistochrone. It turns out that gravity is a manifestation of this fact, in that the definition of "the shortest-time path" takes on a curve when matter is present. This curving of space-time immediately invalidates Newton's first law: Namely that an object at rest must remain at rest or travel in a straight line unless acted on by a force. With gravity, the object cannot obey Newton's first law and must move, even though a force isn't acting on it! The second law also immediately falls, as it states that "the momentum of an object doesn't change without the application of a force." Momentum is equal to the mass times the velocity of the object, but here we're imparting a velocity, simply by the fact that we're near an object, even without touching it! As mentioned previously, in freefall neither you nor the Earth exhibit forces on each other, you just accelerate towards each other. This invalidates Newton's third law.

The entire reason gravity is so weird and scary is because it imparts an acceleration on objects without the presence of a force! It does this by literally changing the rules of the game (by warping the stage, space-time, so that is no longer flat). This is also one of the reasons its so difficult to unify with the other forces.

So, the best thing for your telekinetic physics is to say that it bends space around the object it acts on to cause it to "fall" in the desired direction under the influence of a kind of gravitational field.

When a powerful telekinetic pushes on something, they reach out at the same time, telekinetically and grip space-time. This anchors them in one spot. Then when the telekinetic exerts the force on the object they want to move, the equal and opposite force is applied to the very fabric of time and space. The telekinetic is the fulcrum in this Archimedean simile. I see the consequences of this interpretation as:

The telekinetic can amplify their TK force by anchoring themselves to a very near point in time-space

The telekinetic can amplify their TK finesse by anchoring themselves to a distance point in time-space

The maximum possible force is limited by the strength of time-space. If they try and exert too much TK force then they form a singularity and get sucked into it and poof!

A more skillfull telekinetic can anchor themselves to multiple time-space points, distributing the reaction force they generate so they can exert more force than if the just anchored themselves to one point in time-space

If they don’t anchor themselves to time-space, then when they exert their TK force, they experience the reaction force and levitate/fly/slide/whatever (depending on the direction and the mass of the thing they pushed on)

If they anchored themselves on two points in time-space and pulled really hard they could form a wormhole or time-space tunnel for traveling great distances

$\begingroup$This is the opposite of relativity. The entire point of relativity is that there is no special absolute frame of reference. i.e. you can't be "at rest" in any absolute sense, only with respect to some other object. And that any non-accelerating reference frame is indistinguishable from any other. (And with general relativity, acceleration is indistinguishable from gravity, so you can't tell whether you're in a rocket in space or a constant-speed elevator.)$\endgroup$
– Peter CordesJun 12 at 0:36

$\begingroup$How you explained relativity is entirely correct. And, because we know that relativity is a real thing, we know that there is space-time, and not space and time. Interpreting space-time as an underlying firmament of the universe fanciful, but the discussion is about Telekinetics so I think there is some latitude here for out of the box thinking. By using space-time as an anchor, the psychic is turning the acceleration created into a gravitation force that space-time experiences because remember that if they push too hard, they form singularities. Nothing non-relativistic has been profered$\endgroup$
– EDLJun 12 at 1:30

$\begingroup$No, relativity doesn't require the existence of anything you can "grab on to", in fact it's a strong counter-argument. Relativity is the last thing you should be bringing up if you want to anchor space, i.e. some kind of absolute reference frame. Introducing time as an extra dimension like the 3 known spatial dimensions doesn't help at all; you aren't talking about reaching across time or anything time-based. Calling the collection of space and time "space-time" does not make it a physical thing/fabric with momentum. Your entire answer is totally anti-relativistic (except for point 6).$\endgroup$
– Peter CordesJun 12 at 1:37

$\begingroup$Interacting with (and pushing on) the "background of space" or "spacetime" is fine technobabble and the basis for some SF starships (like the ones in David Weber's Honorverse), but you need to be clear that this is 100% incompatible with Einstein's relativity. (Or at the very least not supported by it at all, and only explainable by very different physics.)$\endgroup$
– Peter CordesJun 12 at 1:41

$\begingroup$@Peter Cordes, You are the only one asserting absolute reference frames. I do not see that as a requirement for what I am putting for. A relative frame is perfectly fine and totally compatible with everything I put out.$\endgroup$
– EDLJun 12 at 1:51

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